The fundamental theorem of asset pricing under transaction costs

This paper proves the fundamental theorem of asset pricing with transaction costs, when bid and ask prices follow locally bounded càdlàg (right-continuous, left-limited) processes. The robust no free lunch with vanishing risk condition (RNFLVR) for simple strategies is equivalent to the existence of...

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Bibliographic Details
Published in:Finance and stochastics 2012-10, Vol.16 (4), p.741-777
Main Authors: Guasoni, Paolo, Lépinette, Emmanuel, Rásonyi, Miklós
Format: Article
Language:English
Subjects:
Arbitrage
Asset pricing
Company insolvency
Costs
Economic Theory/Quantitative Economics/Mathematical Methods
Economics
Equivalence
Finance
Insurance
Literature reviews
Management
Mathematical analysis
Mathematics
Mathematics and Statistics
Price systems
Prices
Pricing policies
Probability
Probability Theory and Stochastic Processes
Quantitative Finance
Statistics for Business
Studies
Transaction costs
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Summary:This paper proves the fundamental theorem of asset pricing with transaction costs, when bid and ask prices follow locally bounded càdlàg (right-continuous, left-limited) processes. The robust no free lunch with vanishing risk condition (RNFLVR) for simple strategies is equivalent to the existence of a strictly consistent price system (SCPS). This result relies on a new notion of admissibility, which reflects future liquidation opportunities. The RNFLVR condition implies that admissible strategies are predictable processes of finite variation. The Appendix develops an extension of the familiar Stieltjes integral for càdlàg integrands and finite-variation integrators, which is central to modelling transaction costs with discontinuous prices.
ISSN:0949-2984
1432-1122
DOI:10.1007/s00780-012-0185-0